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smallsorrow
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 Posted: Sat Oct 11, 2008 9:24 am Post subject: number properties / functions |
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For which of the following functions is f(a+b)=f(a)+f(b) for all positive numbers a and b
A) f(x)=x^2
B) f(x)=x+1
C) f(x)=sq r x
D) f(x) =2/x
E) f(x)=-3x
Pls share your thoughts....
Thank you! |
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vivek.kapoor83
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| Posted: Sat Oct 11, 2008 9:30 am Post subject: |
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IMO E.
coz f(a+b) = f(a)+f(b)
we have to prove.,
then
putiing x=a+b in E
f(a+b) = -3(a+b) = -3a-3b
put x = a
f(a) = -3a
put x =b
f(b) = -3b
f(a)+f(b) = -3a-3b
Hence,E. |
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cramya
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| Posted: Sat Oct 11, 2008 9:44 am Post subject: |
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It should be E
This ha sbeen solved in this forum before but cant find the link
Pick numbers lets say a=2 b=3
f(5) = f(2) + f(3)
x=5, x=2,x=3 WEvaluate the choices and E will be true |
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smallsorrow
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| Posted: Sat Oct 11, 2008 10:44 am Post subject: |
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| e is correct. thanks for explaining! |
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elmiko
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| Posted: Sat Oct 11, 2008 3:45 pm Post subject: |
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| cramya wrote: | It should be E
This ha sbeen solved in this forum before but cant find the link
Pick numbers lets say a=2 b=3
f(5) = f(2) + f(3)
x=5, x=2,x=3 WEvaluate the choices and E will be true |
I don't understand how you plug in the choices into each of the functions in the answer choices. Can you explain further? |
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canuckclint
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| Posted: Sat Oct 11, 2008 5:58 pm Post subject: |
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| elmiko wrote: | | cramya wrote: | It should be E
This ha sbeen solved in this forum before but cant find the link
Pick numbers lets say a=2 b=3
f(5) = f(2) + f(3)
x=5, x=2,x=3 WEvaluate the choices and E will be true |
I don't understand how you plug in the choices into each of the functions in the answer choices. Can you explain further? |
You can plug for example
f(x) = x^2 take a = 2 b = 3
f(a+b) = f(5) = 5^2
not equal to
f(a) + f(b) = f(2) + f(3) = 2^2 + 3^2
Actually there is no need to plug if you got the right answer.
Just remember factoring from algebra.
k(a+b) = ka + kb for any k. just from algebra
Part E is just sucah a case with k=-3
Cheers,
Clinton
Math Minor |
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